Suppose I have multiple identical transformers. Each will drop the supply
voltage down to the utilization voltage. Each has the same capacity and
impedance.
Now suppose I take 2 (or more) of them and wire all the primary windings in
series ... and wire all the secondary windings in series. I fully expect I
will have the same voltage ratio.
But here is my real question. Assuming the supply voltage is the same as
would work with one transformer, what happens to the fault current level
when N transformers are wired in series like this? Assume the supply has
theoretically infinite fault current availability to focus examination of
the fault current to just this transformer arrangement.
This sure sounds like a homework problem. If this is a real problem, what is
the application? Before helping, I would like to know what YOU have done so
far.
Bill
 Fermez le Bushabout two years to go.
 
> Suppose I have multiple identical transformers. Each will drop the supply
> voltage down to the utilization voltage. Each has the same capacity and
> impedance.
>
> Now suppose I take 2 (or more) of them and wire all the primary windings in
> series ... and wire all the secondary windings in series. I fully expect I
> will have the same voltage ratio.
>
> But here is my real question. Assuming the supply voltage is the same as
> would work with one transformer, what happens to the fault current level
> when N transformers are wired in series like this? Assume the supply has
> theoretically infinite fault current availability to focus examination of
> the fault current to just this transformer arrangement.

 This sure sounds like a homework problem. If this is a real problem, what is
 the application? Before helping, I would like to know what YOU have done so
 far.
It is not a homework problem. It is exploring a theory I was told could
not be done, but still suspect that it can be done. What I have "done"
is come up with a theory about what this would do. I'll compare my theory
to what experts say, if/when they say anything about this. I doubt it is
useful for any real applications except for a limited degree of voltage
increase.


If I read what you mean correctly, you are considering the case of N
(V1/V2) transformers with a series connection on both primary and secondary
and using the combination as a V1/V2 transformer providing in the ideal
case no different from a single unit. Since the transformers are not ideal,
all you are doing is increasing the effective impedance of the combination
with respect to a single transformer (you are not increasing the power
rating unless you are applying a higher total voltage which you are not
doing in your question) so the result will be poorer voltage regulation
(more of a voltage drop under load) and a lower short circuit current
compared to a single unit. Total no load current may be lower as flux
density in each core will be lower but otherwise nothing gained.
Sketch the circuit using the mutual inductance model with primary and
secondary electrically isolated rather than the usual T model that is
generally used for a transformer. You should see what is going on.
Total primary R increases. Total secondary R increases.
Higher voltage drops on both sides, for a given I.
Fault current would depend on where/what the fault was.
For example, say the fault is primary shorted to ground.
If it happens in xformer 1 (the one connected directly to
hot) no difference vs if it was the sole xformer. But
if it happens in transformer N, it has all the preceeding
primary windings creating a larger voltage drop, therefore
lower fault current.
Ed
ASSuming the transformer cores don't saturate, the load on each transformer
will be "reflected" back to the primary side.
The reflected impedance will be in the ratio of the square of turns ratio.
If the turns ratio is 1/1 then it's as if the loads were put in series.
The high resistance/impedance load will see higher voltage and the lower
impedance load will see lower voltage. If the voltage drop across the
primary exceeds the voltage rating (plus "margin") the transformer will
saturate twice each cycle and effectively short out for the last part of
each half cycle.
If you want to "solve" the problem, you first solve to nonsaturation and
then determine the saturation point and continue the solution from there.
It's possible the more than one transformer could saturate if you have many
in series.
> Suppose I have multiple identical transformers. Each will drop the supply
> voltage down to the utilization voltage. Each has the same capacity and
> impedance.
>
> Now suppose I take 2 (or more) of them and wire all the primary windings in
> series ... and wire all the secondary windings in series. I fully expect I
> will have the same voltage ratio.
>
> But here is my real question. Assuming the supply voltage is the same as
> would work with one transformer, what happens to the fault current level
> when N transformers are wired in series like this? Assume the supply has
> theoretically infinite fault current availability to focus examination of
> the fault current to just this transformer arrangement.
>

 Total primary R increases. Total secondary R increases.
 Higher voltage drops on both sides, for a given I.

 Fault current would depend on where/what the fault was.
 For example, say the fault is primary shorted to ground.
 If it happens in xformer 1 (the one connected directly to
 hot) no difference vs if it was the sole xformer. But
 if it happens in transformer N, it has all the preceeding
 primary windings creating a larger voltage drop, therefore
 lower fault current.
What if the fault is a bolted short on the secondary terminals right at
the transformer(s)? That should be the worst case other than internal
faults inside the windings, I would think.
 The reflected impedance will be in the ratio of the square of turns ratio.

 If the turns ratio is 1/1 then it's as if the loads were put in series.
 The high resistance/impedance load will see higher voltage and the lower
 impedance load will see lower voltage. If the voltage drop across the
 primary exceeds the voltage rating (plus "margin") the transformer will
 saturate twice each cycle and effectively short out for the last part of
 each half cycle.
The secondaries are also in series, supplying one load.
 If I read what you mean correctly, you are considering the case of N
 (V1/V2) transformers with a series connection on both primary and secondary
 and using the combination as a V1/V2 transformer providing in the ideal
 case no different from a single unit. Since the transformers are not ideal,
 all you are doing is increasing the effective impedance of the combination
 with respect to a single transformer (you are not increasing the power
 rating unless you are applying a higher total voltage which you are not
 doing in your question) so the result will be poorer voltage regulation
 (more of a voltage drop under load) and a lower short circuit current
 compared to a single unit. Total no load current may be lower as flux
 density in each core will be lower but otherwise nothing gained.
 Sketch the circuit using the mutual inductance model with primary and
 secondary electrically isolated rather than the usual T model that is
 generally used for a transformer. You should see what is going on.
I am wanting to confirm my belief that it really would have a lower short
circuit current. But then what I want to do is see what kind of design
would mimic this. I suspect a design intended for a higher voltage, but
used at a lower voltage, would be like that. For example, consider a
transformer with a 7200 volt primary and 240 volt secondary. If it is
supplied with 480 volts, the output should be 16 volts to a light load.
If the transformer impedance is 4%, then the short circuit current would
be within it's loading rating, right?


Bolted short on N transformers  N times the impedance. 1/N times the fault
current. That is what ehjsr and I are trying to say. Draw the circuit setup
with primaries and secondaries isolated from each other not as in the
common T model. It should be fairly apparent then.
Suppose that you have a 7200/240V 10KVA transformer with 4% impedance.
It would have an impedance seen from the primary of 207 ohms (4% of 5184
ohms). It's rated current (primary) would be 1.4A and its short circuit
current would be 35A
Now, at 480V the short circuit current would be 480/207 =2.32A primary which
would be 66%ABOVE its rating (corresponding to (480/7200)*35) meaning that
magic smoke won't appear quite as soon as it would at 35Abut it still
would occur. The open circuit voltage would be 16V as you indicate. You
would have to limit the input voltage to 290V in order to stay within the
1.4A rating.
Changing the transformer base voltage doesn't change the actual impedance.
if you rerated this transformer to 480V, the rated current would still be
1.4A (unless you want to let magic smoke outadmittedly not as soon as at
35A short circuit current) and the % impedance on the new base would be
higher (60%) .
If you stacked a bunch in series as you indicated, then the performance
would be extremely poor. Is this what you want?
I don't see what you expect to gain. A stack such as this is
performancewise and economically, inferior to a properly designed single
unit.
Wrong...
The definition of transformer impedance:
"The percentage of rated primary voltage that will generate rated
current in a shortcircuited secondary."
A 4% transformer with a 7200 volt primary will deliver rated current
to a shorted secondary when the primary voltage is 288 volts.
 Suppose that you have a 7200/240V 10KVA transformer with 4% impedance.
 It would have an impedance seen from the primary of 207 ohms (4% of 5184
 ohms). It's rated current (primary) would be 1.4A and its short circuit
 current would be 35A
 Now, at 480V the short circuit current would be 480/207 =2.32A primary which
 would be 66%ABOVE its rating (corresponding to (480/7200)*35) meaning that
 magic smoke won't appear quite as soon as it would at 35Abut it still
 would occur. The open circuit voltage would be 16V as you indicate. You
 would have to limit the input voltage to 290V in order to stay within the
 1.4A rating.
 Changing the transformer base voltage doesn't change the actual impedance.
 if you rerated this transformer to 480V, the rated current would still be
 1.4A (unless you want to let magic smoke outadmittedly not as soon as at
 35A short circuit current) and the % impedance on the new base would be
 higher (60%) .
OK, maybe I have to take this a step further ... 240 volts in, 8 volts out.
 If you stacked a bunch in series as you indicated, then the performance
 would be extremely poor. Is this what you want?
What is the difference between one transformer rated 15000 VA, 7200 volts
primary, 240 volts secondary, 4% impedance ... and ... 30 transformers rated
500 VA, 240 volts primary, 8 volts secondary, 4% impedance, wired with both
primary and secondary in series as I've described (besides the latter being
a rats nest).
How many primary winding turns would the former need to have? How many
would the latter need to have? Would the latter times 30 equal the former?
One of the things that got me thinking on this was seeing a pole pig near
a road, dedicated powing a few lights on a sign. I figured there was not
more than a couple KW of light there, if that. The pole pig was rather
small. Yet I was trying to imagine what kind of primary winding it would
have given that it was probably being supplied with no less than 7200 volts.
And I was thinking that, as the KVA rating goes down, number of turns goes
up, and at voltages of 7200 and up, that's going to soon reach a point where
the size can't get smaller because of the heavier insulation needed with
the many turns (though I suppose if very carefully designed, not so much
insulation would be needed between adjacent turns).
 I don't see what you expect to gain. A stack such as this is
 performancewise and economically, inferior to a properly designed single
 unit.
And it may not be the economical way even for what I have in mind, which
is to power a load which will approach being a short circuit, such as an
electric arc. But I am only thinking about this in a theoretical sense
because I did not believe it when someone told me it was not possible to
make a transformer that would convert a voltage, limit the current, and do
this within it's load handling capacity, without using an additional pure
inductance in series with the secondary. Well, I think it certainly is
possible. Maybe what they meant is: it is not ecomically practical.
How much will the power meter spin if the load side terminals are bolted
together in a short circuit (before magic smoke gets out)? I would think
not much if any because there's no appreciable voltage. Depending on the
fault current taking place, it can still dissipate some heat, perhaps quite
fast. It would be an interesting race to see who lets the magic smoke out
first: the meter, the wiring, or the transformer.
 
>>
> If I read what you mean correctly, you are considering the case of N
> (V1/V2) transformers with a series connection on both primary and secondary
> and using the combination as a V1/V2 transformer providing in the ideal
> case no different from a single unit. Since the transformers are not ideal,
> all you are doing is increasing the effective impedance of the combination
> with respect to a single transformer (you are not increasing the power
> rating unless you are applying a higher total voltage which you are not
> doing in your question) so the result will be poorer voltage regulation
> (more of a voltage drop under load) and a lower short circuit current
> compared to a single unit. Total no load current may be lower as flux
> density in each core will be lower but otherwise nothing gained.
> Sketch the circuit using the mutual inductance model with primary and
> secondary electrically isolated rather than the usual T model that is
> generally used for a transformer. You should see what is going on.
>
>I am wanting to confirm my belief that it really would have a lower short
>circuit current. But then what I want to do is see what kind of design
>would mimic this. I suspect a design intended for a higher voltage, but
>used at a lower voltage, would be like that. For example, consider a
>transformer with a 7200 volt primary and 240 volt secondary. If it is
>supplied with 480 volts, the output should be 16 volts to a light load.
>If the transformer impedance is 4%, then the short circuit current would
>be within it's loading rating, right?

 Wrong...

 The definition of transformer impedance:

 "The percentage of rated primary voltage that will generate rated
 current in a shortcircuited secondary."

 A 4% transformer with a 7200 volt primary will deliver rated current
 to a shorted secondary when the primary voltage is 288 volts.
OK, my numbers were a bit off (not sure where I goofed the arithmetic).
But I had the concept.
Now I shall build (in my mind) a transformer (array) that will have a
maximum fault current of somewhere in the range of 1 to 5 milliamps,
using step up instead of step down.
 Bolted short on N transformers  N times the impedance. 1/N times the fault
 current. That is what ehjsr and I are trying to say. Draw the circuit setup
 with primaries and secondaries isolated from each other not as in the
 common T model. It should be fairly apparent then.
It is apparent. It seemed that way long before I first posted this. But
I wasn't sure if I had overlooked some other concept that would get in the
way (besides the economic practicality issue). So I asked. Seems to be
nothing unexpected would get in the way.

Ideally, same short circuit current would flow. Difference is in the
nonideal problems.


YesIF the core cross section was the same. It may not be this depends on
the design criteria which typically are not the same for a 500VA 240/8V
transformer as for a 15KVA 7200/240V transformer. I would also expect that
the total iron in the 30 transformers would be greater. I expect that,
without having done the calculations, that the total volume of the multiple
transformers would be greater (a 5KVA 7200/240V transformer is very nearly
the size of a 5KVA 240/240V transformer because the core is dominant) as
well as still having to put extra insulation conductor to case and primary
to secondary in the hot end transformers (or float the caseusing external
insulation but this won't help with primary to secondary voltages. In other
words for the top transformer of a stack, there is a voltage difference
between primary and secondary which is 7200+/8V compared to 7200+/240V in
a single transformer. Now one could use different insulation levels in each
of the 30 transformers essentially grading the insulation (as is often
done with EHV transformers) but this means 30 different transformers which
would be impractical. This works within limits but does present problems in
the case of surges because grading adversely changes the capacitive
distribution and the surge voltage distribution.
However, at the 7200V level, the insulation requirements are so little in
excess of the requirements at 240 V (in terms of size) that the above is all
rather moot.
What may not be moot is the 56 extra connections between transformers.


Actually the KVA wont determine the number of turns  one could have 30:1
turns, 60:2 turns, etc.
A transformer design is based on its expected use. Of course too low a turns
ratio may not be desirable A 5KVA pole pig will have maximum efficiency at
or near 1/2 load as that is where its average load is. A station transformer
will generally have maximum efficiency at or near full load. There is a
balance between core losses (core volume) and copper losses which determines
the point of maximum efficiency. However, actual efficiency can be changed
by spending more money.
So far the figures don't indicate this. If you have a transformer with a
high leakage inductance (no external inductor needed) you can get limiting
( a gap in the core helps)  A neon lamp transformer is an example.
Typical power transformers are designed, in general for low leakage (in your
case that is 4% leakage impedance). The cost of high impedance is poor
voltage regulation. I other words you get low short circuit current by
making a lousy transformer.

The race would be interesting but what you get will depend on the HV supply.
If you have the worst case a fixed 7200V at the supply, the short circuit
current will be 25 times rated current and the short circuit input KVA would
be 25 times the rating (375KVA). The real power would likely be about 10% of
this or about 37KW. so the meter will spin quite well before it fails. If
the incoming supply has 4% impedance then the fault current and KVA will be
about 1/2 of the above.
As far as your objective of limiting current to the rated current probably
you should be looking at how welding transformers are designed. They are
rated on a different basis than normal power transformers as they are not
used as normal power transformers. 
Don Kelly snippedforprivacy@shawcross.ca
remove the X to answer

 As far as your objective of limiting current to the rated current probably
 you should be looking at how welding transformers are designed. They are
 rated on a different basis than normal power transformers as they are not
 used as normal power transformers. 
I would guess they have a different way of limiting current, such as extra
inductance. For things I want to experiment with, that may well be the way
to go.
That works but there are alternatives which would be useful if one is
building many units. One way is to design so leakage reactance is relatively
high. On open circuit the voltage would be normal but on load, the voltage
regulation would be poor essentially limiting short circuit current.
Probably cheaper than a normal transformer as one could skimp on core
material.
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